No, when an engine is first started, it needs to get to operating temperature as quickly as possible. Since you have two fans (I'm assuming they're both electric) you'll find that one is dedicated to cooling the radiator and the other is dedicated to cooling the condenser, part of the air conditioning system. If you aren't overheating, I wouldn't worry about fan function.

Today's cars are built to be more durable and handle more wear and tear. This includes handling more heat. The fans your referring to won't come on unless the temp reaches a set limit. Only then will this fan activate. The 2nd fan is for your a/c cooling system and when the a/c is on this fan is also.

You are probably going to get lots of opinions from mechanics more qualified than me, but in my experience, the fan doesn't always start right away becvause the engine is not yet hot enough.

NORMALLY, the only time you see that is when you have the A/C turned on. Otherwise, the fan only turns on when the engine temp goes beyond approximately 215 or so, depending on the make of car.

The fans will come on when your engine comes up to the proper temperature. Then they will go on and off as engine temp changes.

Yes

When I start my car isn't there suppose to be a fan that kicks on immediately? When I looked under the hood today I noticed there wasn't any fans going. I know there's two fans, isn't one on continuously on while the other one kicks on occasionally.